4 From Casimir Forces to Black-Body Radiation: Quantum and Thermal Fluctuations

The problems we are working on right now do have the potential to completely change the way that we think about energy.

The idea of achieving higher energy efficiency, of using every drop of energy at our disposal, is definitely revolutionary, though the world is moving in that direction. Greater energy efficiency will revolutionize the way we view ourselves and our relationship to energy, technology, and the environment.

—Alejandro W. Rodriguez

Alejandro W. Rodriguez is Assistant Professor of Electrical Engineering, Department of Electrical Engineering, Princeton University. He received his doctoral degree in physics from MIT in 2010. Prior to joining Princeton University, he held joint postdoctoral positions with the School of Engineering and Applied Sciences at Harvard University and the Department of Mathematics at MIT.

He has received several awards, including the National Science Foundation Early Career Award, the MIT Infinite Kilometer Award, and the MIT Orloff Award for Service in Physics. He is also a National Academy of Sciences Kavli Fellow (2014) and was named a World Economic Forum Global Shaper (2011–2013).

About himself, he says:

I was born in Havana, Cuba, a by-product of loud rumbas, a family of physics enthusiasts, and Afro-Cuban folklore. At age twelve I emigrated to the United States. Although my last name is Rodriguez-Wong, a reflection of my dual Cuban and Chinese ancestry, I generally publish under the name Alejandro W. Rodriguez. When I am not thinking about photons, I am either dancing salsa, watching old films, listening to Cuban music, or playing video games.

Adolfo Plasencia:

Alejandro, thanks for meeting me.

Alejandro W. Rodriguez:

Thank you for coming.

A.P.:

Today, we are in the Physics Department at MIT. You were, however, born in Cuba.

A.W.R.:

Yes, I’m Cuban.

A.P.:

How does one get from Cuba to the Physics Department at MIT?

A.W.R.:

Well, to be honest, my family instilled in me a love of science. My dad studied physics. My mother studied astrophysics. My stepfather was a physics professor at the University of Havana. They never forced anything on me; to like physics you have to get to know it, try out a physics class. They did, however, instill in me a love of science in general. After arriving in the United States, from high school and even before that, in preschool in Cuba, I fell in love with physics and I firmly decided already in my second year at high school that I was going to come to MIT.

A.P.:

Is there anyone, any professor, you have met who has been decisive for your getting involved in this field of physics?

A.W.R.:

I did my undergraduate studies and started research here at MIT as well. During those three years I interacted a lot with professors whom I work with today, and I wasn’t absolutely sure what I was going to like most. I knew I liked theoretical physics, but I ended up working in a new kind of physics, partly computational and partly theoretical. The convergence of these two areas is what made me decide in the end; obviously, the love I felt for the intersection of physics and computing is related to the relationship with my adviser at MIT, Steven G. Johnson, and also with John D. Joannopoulos. They are two professors who had a big impact on me and started me out on this path.

A.P.:

Why did you move toward quantum physics on a nanoscale and not toward the physics of the universe, for instance? Why the infinitely small universe and not the big one? Why between 0 and 200 nanometers?

A.W.R.:

There are two reasons. When I started my degree I was in love with general relativity, which you know is related to astrophysics, to the macroscopic world, and to hugeness, but at MIT there’s quite a practical environment. There are many theorists; theory is very strong at MIT. But then there are people around you who are always thinking about applications and how to help society by exploiting technology, by thinking about specific applications. This ideas approach to science is what made me view quantum mechanics or the nanoscale world as a source, where I felt that my work could have a more direct impact on everyday technology. It isn’t that astrophysics and general relativity are not important for society or technology but that quantum physics has a much broader connection to everyday things.

A.P.:

Let’s speak about the Casimir forces. I remember a news item reported on the MIT website under the title “Mysterious quantum forces unraveled,” which cited your work.¹ What mysterious forces had you unraveled?

A.W.R.:

Casimir forces were discovered a long time ago. In 1948 Hendrik Casimir, a physicist, discovered that if you have two neutral objects—that is, they have no electrical charge—placed a few nanometers apart, they will attract one another. In classical physics, the absence of an external current also means that no field exists between the two objects, and theoretically there would be no force between them. There would be no reason for any interaction at this scale. We’re talking about a mysterious attraction in the sense that it cannot be easily explained by classical laws. It occurs because electromagnetic waves, or light, permeate the vacuum. The vacuum is not empty.

A.P.:

The vacuum is not nothing. …

A.W.R.:

Exactly. It is not nothing.

A.P.:

And is there also energy within a vacuum?

A.W.R.:

There is energy in the form of “virtual photons.”

A.P.:

But can photons be virtual?

A.W.R.:

Yes, of course. Then again, they’re not so “virtual” when they have so many physical ramifications, when you can observe their existence. They are called virtual because they come from quantum mechanical processes, from Heisenberg’s uncertainty principle, which reveals quantum features that aren’t explained by Newtonian mechanics. Heisenberg realized that the rules of probability governing subatomic particles are born from an apparent paradox, whereby a particle’s position and momentum, its rate of movement, cannot be simultaneously measured with perfect precision. Besides, according to this principle, on a quantum scale the mere act of observing changes what you are observing. As a result of this uncertainty, the world at small scales is chaotic and filled with fuzziness: there is much movement. Consequently, charges on atoms, the microscopic charges that exist in neutral objects, interact with each other through the laws of quantum mechanics.

A.P.:

Theoretically, entropy gets worse, never better; or do physicists want to turn things round and make entropy get better?

A.W.R.:

In this case, we are talking about a thermodynamic system that is in equilibrium; entropy by definition doesn’t change. But yes, the idea is that we are trying to get hold of this disorder, this electromagnetic chaos, and do something useful with it. We are trying to understand it to see if we can develop some technology and get something innovative out of this chaos.

A.P.:

Alejandro, the people who read this will think we’re talking about things that sound a bit alien.

A.W.R.:

About crazy things. …

A.P.:

Crazy, yes. But anyone who has an iPhone knows that if it is rotated, the screen automatically changes from vertical to horizontal. This is due to micromachines, such as accelerometers, which are related to these Casimir forces. In other words, there are already applications being used by ordinary people. Don’t you agree?

A.W.R.:

Yes, these forces have already been measured experimentally. Over the last four decades, dozens of experiments have been performed that have precisely measured Casimir forces. As technology continues to advance and the size of devices gets smaller, Casimir forces will play a much more prominent role. Right now there are devices with parts that function by taking advantage of these forces. But what produces the Casimir forces in the devices has nothing to do with gravity. Basically, these forces are the result of quantum mechanics and the electromagnetic field. Nevertheless, they are having a big impact on the macroscopic devices that we regularly employ.

A.P.:

With Heisenberg’s uncertainty principle, everything has become blurred, hasn’t it?

A.W.R.:

Exactly. The particle doesn’t have a specific volume that is fixed and static in space. You can only state the probability of it being in a particular location, viewing the particle as a wave, not as a corpuscle. And by approaching it with quantum rules and wave dynamics, the strange behaviors we observe make more sense.

A.P.:

To make sense for you in this way, maybe you were lucky to have been born after and not before Einstein because it would have been scientifically subversive to say these things eighty years ago, don’t you think?

A.W.R.:

Absolutely. For instance, there were physicists who believed that God didn’t play dice, and Einstein was one of them.² Indeed, the consequences of quantum mechanics are very strange; it’s very different from the macroscopic world that we experience on a daily basis.

A.P.:

You don’t talk about it as though it were anything strange. For you is it now?

A.W.R.:

It seems natural to me now. For me now, the strange thing would be if quantum mechanics didn’t exist. But this isn’t trivial; it takes time to warm up to it. At this moment, I don’t understand everything about quantum mechanics, but this ignorance is not ignorance of the theory of quantum mechanics but rather of how the world functions so strangely at such scales. The same ignorance concerning quantum mechanics is also still professed by some other physicists.

A.P.:

There’s something else I find very interesting. First there was a person, a theoretical physicist thinking about something; then there was somebody like Higgs. Many decades and billions of dollars or euros went into building an accelerator to find a particle that theory said existed. Now there are thousands and thousands of scientists in Europe working in a huge tunnel, where it seems to have finally been found, and Peter Higgs and François Englert were awarded the Nobel Prize in Physics in 2013. What’s your opinion on this?

A.W.R.:

I think this is part of science. The positron is an elementary particle, the antiparticle of the electron. Its existence was predicted by Paul Dirac in 1928. It was first discovered theoretically and later experimentally in 1932 by the North American physicist Carl David Anderson from photographs of the trail left by cosmic rays passing through a cloud chamber. In the scientific school that existed two hundred to three hundred years ago, experiments basically yielded to theory. Today we are in an age where theory is, in certain cases, much more advanced than experiments. And it is important to work on this kind of fundamental physics. Therefore, I do agree with people investing their money and time in studying fundamental physics. Nobody can tell you, “Look, this is what physicists should be working on; this is the branch of physics that matters,” because history tells us something completely different. Sometimes the ideas that appear to be less important turn out to be the most revolutionary. A simple example is the laser.

A.P.:

I met you at MIT. Now you are conducting research at another distinguished institution, Princeton University, on the campus where the Institute for Advanced Study is located. Here Albert Einstein worked and lived, as did many other physicists and mathematicians, such as Kurt Gödel, J. Robert Oppenheimer, and John von Neumann, etc. It’s undoubtedly a great place for a physicist.

Although you haven’t fully put the Casimir forces to one side, I know that you are researching questions related to power fluctuations of the electromagnetic field.

It also sounds exotic.

Can you briefly explain the topics you are currently working on?

A.W.R.:

My field of interest is optical fluctuations. Electromagnetic fluctuations include two types of processes: quantum processes and thermal processes. They are both important and are manifested in different ways. When devices are made smaller and smaller, these interactions become more and more important. We spoke about quantum fluctuations and how they lead to forces between objects. So, just as fluctuations lead to forces between objects, they can also lead to energy exchange between them. Planck, Kirchhoff, and other scientists in the late 1800s and the beginning of the 1900s developed the theory of thermal emission, related to fluctuations—the same kinds of fluctuations that lead to Casimir forces.

Just as in the case of Casimir forces, thermal fluctuations depend on the properties of materials and the shapes of the emitting objects. When you’re looking at thermal radiation from an object into the far field—and this was well known in the 1900s—there is a maximum amount of thermal radiation that an object can emit, called a black-body limit.

A black body is a theoretical object that can emit with perfect efficiency into the far field. It doesn’t exist in reality. It is also well known that if you have perfect emission, then you have to have perfect absorption. Therefore, a black body is an object that can perfectly absorb every ray of light coming into it at every frequency. We have this concept of a black body, which doesn’t really exist in nature because no object can absorb light perfectly at every single frequency. This relationship between perfect absorption and perfect emission of thermal radiation was used for many decades and continues to play a key role in the design of solar absorbers and thermal emitters.

For example, the relationship is very important for solar photovoltaics and thermal panels for solar harvesting—in other words, for energy harvesting. It’s basically prevalent in every single technology related to solar energy. The goal of solar absorbers and thermophotovoltaics is to create objects that can absorb radiation perfectly over some range of wavelengths so that this energy can be converted into electricity. This essentially uses the same ideas that physicists had developed over a hundred years ago, which we are using now to design surfaces and objects that can absorb light very efficiently and therefore emit light very efficiently, that is, thermal absorbers. However, our understanding of how to create a black body over a certain range of wavelengths is a work in progress. This applies to most objects. For example, if you take a piece of copper or gold, then that object is barely a perfect absorber and therefore doesn’t have good emission properties. Instead, we design the surface of the object. We structure the surface of the gold or copper so that by changing the geometry, an object can be created that is as close as possible to a black body over some desired range of frequencies.

Until recently, it was believed that the maximum heat transfer between two objects would also be limited by the black body limit. However, in the 1950s Dirk Polder and Van Hove carried out a calculation in which they took two planar objects, one at a hot temperature, T1, and the other at a colder temperature, T2, and investigated their mutual heat transfer. Here, heat transfer refers to the heat radiated by the hot object and absorbed by the cold object, which varies as a function of the amount of separation between the two objects. They observed that as the objects got closer and closer to each other, below what we call the thermal wavelength—which is a wavelength associated with the higher of the two temperatures—you get hundreds to thousands of times more heat transfer from the hot object to the cool object, even going way beyond the black-body limit. Therefore, when you bring two small objects together, the heat transfer from one to another can exceed the black-body limit, which was established by Planck in the 1900s, by orders and orders of magnitude; it could be a billion times more. So you can actually extract a lot more energy from an object by putting it in the near field of another object than you would in the far field. By the near field I mean a very small separation exists between the two objects, in the micrometer range or smaller. Hence, just as Casimir forces increase significantly and are magnified at short length scales, so is energy transfer.

This was a revolutionary idea because now you’re not limited. When you bring two small objects together at nanometric and micrometric separations, you can get heat transfers that are significantly larger than the black-body radiation limit.

A.P.:

Why is this field of quantum and thermal fluctuations important in practice, and what likely impact do you think it will have with respect to real technological applications in the future?

A.W.R.:

We know that over the past sixty years, optics has revolutionized many industries, including telecommunications and information technology. It is responsible for breakthroughs in medical science. The key is that we can manipulate light in very precise ways to control how it interacts with devices and how it behaves. But as you scale these systems and devices down to smaller and smaller sizes, it turns out that even the tiny fluctuations of matter—matter is constantly vibrating; there are charges, electrons and atoms—create optical fields and optical waves and electromagnetic fields whose interactions can no longer be neglected, whose interactions themselves can lead to interesting effects at those scales.

One of these effects is known as the Casimir effect, which involves electromagnetic fluctuations given off by matter as the matter vibrates, causing interactions or forces between objects, thus pushing objects away from or toward one another.³ A vacuum is full of fluctuating electromagnetic fields. These are optical fields, released by the vibrations of matter, that persist even when the temperature of the materials is absolute zero, even when the only remaining source of fluctuations and vibrations is quantum mechanical and is due to the uncertainty principle. So what we are studying is just the familiar glow of matter, but we’re studying the effects that result from the fact that these electromagnetic fields are everywhere.

I think there is great potential for the field. Just as we learned how to manipulate laser light to confine photons and to get information from one place to another, there is a lot to be done through harnessing and controlling quantum and thermal fluctuations by designing structures at the nanoscale.

A.P.:

This revolutionary idea you’ve spoken about still hasn’t reached the devices being used, but to make a projection, which areas of future applications are you thinking about in relation to the research you are conducting?

A.W.R.:

One, for instance, is in the field of thermophotovoltaic energy generation.⁴ A thermophotovoltaic device involves two objects. One is operating at a very high temperature, so it’s heated either by heat, such as from the Sun or from a thermonuclear reactor, to a very high temperature, usually greater than 2000 Kelvin. The other object is an absorber, which is usually some kind of semiconductor with a band gap. The absorber absorbs the radiation coming from the hot object and converts it into electricity. That’s the basic idea behind a thermophotovoltaic device. But all such devices currently operate with objects in the far field; that is, the emitters and absorber are very far apart, separated by hundreds of microns or more. Therefore, they are not taking advantage yet of the fact that as these objects are brought closer to one another, the heat transfer can be significantly larger, many times greater than the black-body limit.

The question, therefore, is whether or not our current theories and understanding of heat transfer will be able to make an impact on future thermovoltaic technology. I think it is very likely that it will because vast amounts of energy are embedded in material fluctuations that are not being exploited. Another application of heat transfer in the near field is cooling.

A very recent experiment, from 2015, demonstrated this idea. It showed that if you take a hot object and bring it close to a cold one, you get heat transfer from the hot to the cold object, and that heat transfer is essentially acting to cool the hot object because it is energy being released by the hot object. Every second that the Sun emits radiation to the Earth it is losing energy; thus the Sun is getting cooler with time, and at some point it will run out of energy as it will have released all of its energy in the form of thermal fluctuations. The same thing happens at the nano- or microscale. If you bring an object near a hot one, the cool object will act as a coolant; it will take heat away from the hot object. The more heat you can collect from the hot object, the more you cool it. So the idea that you can bring objects close together and absorb these thermal fluctuations more efficiently in the near field certainly has applications.

For example, in a computer or laptop, as transistors get smaller, their functionality is limited by effects associated with overheating, and a lot of energy is spent keeping the systems in your computer cool. If we could figure out a way to use this near-field heat transfer mechanism to absorb the heat and dump it into another system, a cooler system, this would have a big impact. Heat transfer and radiation have also been recently proposed as means to cool homes by taking advantage of the cosmos; it would work by dumping energy from hot objects here on Earth into the vacuum in space. This idea is not crazy at all and in fact was experimentally verified this year.

A.P.:

Today, on the International Space Station, no one would consider using any energy that wasn’t solar. On Earth, however, we have long been tied to fossil fuels such as crude oil, and renewables make up only a small part of the energy we use.

Do you think that in the medium and long term, these types of revolutionary areas you’ve been researching have the potential to change the relationship between people and the energy we use?

A.W.R.:

I do think so, to a large degree. It’s interesting that you mention space exploration and space technology taking advantage of solar energy to perform work. One of the systems used in space satellites is already taking advantage of the idea we’re discussing, not necessarily of the enhanced near-field heat transfer that occurs between objects when you put them very close together but rather exploiting thermophotovoltaics, by heating up the emitter and using the energy that radiates from the emitter to the absorber to do work, to convert the energy to electricity. In fact, some of the thermophotovoltaic devices used in satellites employ thermonuclear reactors whose sole purpose is to heat up the thermophotovoltaic emitter. This is basically the way you convert thermal energy into work, into electricity. However, on Earth we have an abundance of solar energy, which means we would essentially be using the Sun to heat up these objects for us.

The problems we are working on right now do have the potential to completely change the way that we think about energy. Many of the systems that we use today are very inefficient in that a lot of energy is wasted as heat. I just mentioned the transistors and other devices inside computers, which typically release a lot of heat; much of this energy is unused and wasted. The problems we are discussing and the questions we are addressing revolve around how to use this otherwise wasted energy, which hasn’t been tapped for centuries, at least not fully, and recycle it.

How do we use that thermal fluctuation, those thermal energy sources, to continue to do work, so as to make our systems more efficient?

However you want to think about it, whether in terms of cooling the system and increasing its efficiency or in terms of using the energy source and converting it into electricity, the basic idea we are working toward is that of using wasted energy (heat) and reusing it to do useful things.

Therefore, the idea of achieving higher energy efficiency, of using every bit of energy at our disposal, is definitely revolutionary, though the world is moving in that direction. Greater energy efficiency will revolutionize the way we view ourselves and our relationship to energy, technology, and the environment. Until very recently, efficiency wasn’t one of the biggest metrics we used to gauge success; instead, we viewed technology through the lens of functionality. We wanted to create technology to function in a particular way, and sometimes it didn’t matter how we got there. There is a growing movement to develop new technologies that not only expand functionality but also achieve higher energy efficiency. Every time we extract matter and energy from our planet, we want to make sure that all of it is being used for something that is useful.

Heat, in the form of thermal radiation, is a by-product of many of the technologies that we use today. My goal is to try to harness it and make it work for us.

A.P.:

With respect to this revolutionary change driven by discoveries, and the ideas you’re explaining, do you think a change in thinking about energy expenditure will be necessary to take advantage of the scientific discoveries that are now emerging?

A.R.W.:

To a large degree there has already been a significant change in attitude about what we think of as a good technology.

There is actually a scientific movement right now that is moving closer and closer to the ideal I just articulated. More and more scientists and engineers are viewing themselves as agents of change and creators of technologies that operate on the basis of sustainability and higher standards of efficiency, which is essentially what I’ve been talking about. These metrics are being prioritized in many ways. Much work remains to be done in this area, and much remains to be proved. That is true, however, of any science that is still maturing. We do need more people to champion this cause and to recognize that by funding and supporting this kind of research, we as a society are making a statement about our priorities. I think to a large degree this is already the case.

It is very important that many people, both inside and outside the scientific community, understand why this type of research is crucial for our future, why it is “visionary” and decisive for our future relationship to energy and the environment, and why that relationship must be different and better than it has been so far.

A.P.:

Thank you very much, Alejandro!

A.R.W.:

You’re welcome. It was a pleasure.